import matplotlib.pyplot as plt import numpy as np import seaborn as sns  def fractile(l, p, C):     """Find the p'th fractile of l for various interpolation schemes.     All schemes are linear but vary in their definition of the range     of the CDF.          Args:         l (numpy.array): The array of numbers to find fractiles for.         p (numpy.array): The fractiles of interest (as floats between 0 and 1).         C (float): Interpolation scheme, given as a float between 0 and 1.             0 corresponds to what Excel's PERCENTILE.EXC calculates.             1/2 corresponds to what MATLAB does.             1 corresponds to what NumPy/Excel's PERCENTILE.INC calculates."""     def get_index(N, p, C):         the_index = (N + 1 - 2*C)*p + C - 1         return the_index.clip(0, N-1)     s = np.sort(l)     x = get_index(len(s), p, C)     s = np.append(s, 0)  # For C < 1, we add a dummy value to s to take care of the case x = N-1.      return s[np.int_(x)]*(1-x%1) + s[np.int_(x)+1]*(x%1)  x = np.array([15, 20, 35, 40, 50]) p = np.arange(0, 100.1, 0.1)  for v in (0, 0.5, 1):     plt.plot(p, fractile(x, p/100, v))  plt.title('Three different linear interpolation schemes') plt.xlabel('Percent rank') plt.ylabel('Percentile value') plt.xlim(0, 100) plt.ylim(14, 51) plt.legend(['$C = 0$', '$C = 1/2$', '$C = 1$'], loc='lower right') plt.savefig('percentile_interpolation.png', dpi=400)